## Propagation of analytic singularities up to non smooth boundary.(English)Zbl 0666.58043

Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 7, 9 p. (1987).
Let M be a real analytic manifold of dimension n, X be a complexification of M. $$\Omega$$ be an open subset of M. The author gives the definition of a microsupport, which coincides with the classical analytical wave front set over $$\Omega$$, but it may be strictly larger than its closure in $$T^*M$$. Let P be a differential operator on X, u a hyperfunction on $$\Omega$$ solution of the equation $$Pu=0$$. Under some conditions on the principal symbol $$\sigma$$ (p) it is proved that $$p\in SS_{\Omega}(u)$$ implies $$b^+_ p\in SS_{\Omega}(u)$$, where $$b^+_ p$$ is the positive half integral curve of the real Hamiltonian vector field which corresponds to the function Im $$\sigma$$ (p).
Reviewer: M.Novickij

### MSC:

 58J47 Propagation of singularities; initial value problems on manifolds

### Keywords:

analytical wave front; microsupport; principal symbol
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